Algebra Examples

$2 \ln (e^{\ln (5 x)}) = 2 \ln (15)$

Step 1

Exponentiation and log are inverse functions.

$2 \ln (5 x) = 2 \ln (15)$

Step 2

Divide each term in $2 \ln (5 x) = 2 \ln (15)$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 \ln (5 x) = 2 \ln (15)$ by $2$ .

$\frac{2 \ln (5 x)}{2} = \frac{2 \ln (15)}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 \ln (5 x)}{2} = \frac{2 \ln (15)}{2}$

Step 2.2.1.2

Divide $\ln (5 x)$ by $1$ .

$\ln (5 x) = \frac{2 \ln (15)}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ .

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Step 2.3.1.1

Cancel the common factor.

$\ln (5 x) = \frac{2 \ln (15)}{2}$

Step 2.3.1.2

Divide $\ln (15)$ by $1$ .

$\ln (5 x) = \ln (15)$

Step 3

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$5 x = 15$

Step 4

Divide each term in $5 x = 15$ by $5$ and simplify.

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Step 4.1

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $5$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $15$ by $5$ .

$x = 3$